Let's say 3 x 2 = 6. Three is how many kids there are in a 'group.'
Two is how many 'groups' there are, and six is the answer. Now let's
say 3 x (-2) = -6. How can you have negative two 'groups' of three
kids?

Does the distributive property contradict the rules of order of
operations? When we have a(b + c) order of operations says we should
add first in the parentheses, then multiply, but the distributive
property says we can multiply first to get ab + ac, then add.